Question

‘a’ and ‘b’ are two positive integers such that $a^b\times b^a=72.$ Find a + b.

• A. 1
• B. 8
• C. 5
• D. 6

Answer 1

The correct option is C 5

The number 72 can be factorized as
$72=2\times 36$
$36=2\times 18$
​​​​​​​$18=2\times 9$
​​​​​​​$9=3\times 3$
i.e.,​​​​​​​ $72=2\times 2\times 2\times 3\times 3$
$72=2^3\times 3^2$
So, a = 2, b = 3
a + b = 2 + 3 = 5